Anthony Martial scored the only goal as United moved into the top five to keep their hopes of Uefa Champions League qualification alive.
But Van Gaal said: “It was more or less a stolen victory. We were today the lucky team. We didn’t play so well, it looked like we were not fresh. We have only created two chances.”
Read more from Richard Jolly:
United made it back-to-back wins following a derby triumph against Manchester City two weeks earlier and continue their pursuit of their neighbours.
Van Gaal added: “It was very important to win today otherwise the victory against City was worthless. We keep in touch with City, one point behind. We keep in touch with Arsenal, five points behind. We have to play Tottenham [next Sunday].
“It is not easy but normally we are playing very well against the top teams. If we continue like that I am very happy.”
Van Gaal praised the summer signing Martial, 20, for his performance and goal, saying: “It is fantastic what he is doing.”
The United manager dedicated the win to director Sir Bobby Charlton after Old Trafford’s South Stand was renamed in honour of the 78 year old.
“It was a privilege for a Dutchman to see how the English culture respect all the players,” he said.
“It is marvellous to see. You see a standing ovation for Sir Bobby there were some tears in my eyes. He was an idol of mine when I was youngster growing up in Holland.”
Defeat was Everton’s third in as many league games and leaves them 12th in the table and they were booed off by a section of their supporters.
Manager Roberto Martinez said the players share the fans’ disappointment, explaining: “You can hear our boos in the dressing room.”
Follow us on Twitter @NatSportUAE
Like us on Facebook at facebook.com/TheNationalSport